I suggest that you try shooting a 7mm mauser rifle (also known as 7x57). Dates from 1892 or so, doesn't kick much for a high power rifle, and can be had for not too much money. You can even find some that are available without paperwork, since some were made before 1898.

Rumor has it that "Famous African Hunting Guides" would keep one around to loan to clients who brought big manly rifles and got too recoil shy to hit anything.

If that is too much for you, you should try to borrow a Martini cadet in .310 cadet, although you might have to mortgage your house for ammunition. Those 4 lb. rifles are sweet. They were originally used to teach 14-year-old cadets (in the British empire Victorian era) to shoot a rifle that functioned like a miniature Martini-Henry. Some have been "converted" to 32-20, some to 38 special (or 357), with more or less success. They were also popular as a base for conversion to other calibers and custom rifles.

Other choices for the recoil shy include pistol caliber lever actions (except lightweight 44 magnums), and anything in 223.